The phrase "to back the manager" means to support and trust the decisions and actions of the person in charge, usually in a workplace or sports team. Full definition
But nothing can be done if the owners don't back the manager. (justarsenal.com)
But is it the right time for clubs to twist by chopping and changing, or stick by backing the manager with funds in the transfer market. (caughtoffside.com)
Try backing the manager of the team you support because it's the only reality there is. (justarsenal.com)